Brief Communication | Published:

Laser optics

Fractal modes in unstable resonators

Nature volume 402, page 138 (11 November 1999) | Download Citation



One of the simplest optical systems, consisting of two mirrors facing each other to form a resonator, turns out to have a surprising property. Stable resonators, in which the paths of the rays are confined between the two mirrors, have a well known mode structure (hermite–gaussian), but the nature of the modes that can occur in unstable reson-ant cavities (from which the rays ultimately escape) are harder to calculate, particularly for real three-dimensional situations1. Here we show that these peculiar eigenmodes of unstable resonators are fractals, a finding that may lead to a better understanding of phenomena such as chaotic scattering and pattern formation. Our discovery may have practical application to lasers based on unstable resonators1.

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    • G. P. Karman

    Present address: Philips Research Laboratories, Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands


  1. *Leiden University, PO Box 9504, 2300 RA Leiden, The Netherlands e-mail:

    • G. P. Karman
    • , G. S. McDonald
    •  & J. P. Woerdman
  2. †Blackett Laboratory, Imperial College, London SW7 2BZ, UK

    • G. S. McDonald
    •  & G. H. C. New


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